Theory of the Static Stability of Cylindrical Domains in Uniaxial Platelets

Abstract

A theory of the static stability of circular cylindrical domains in uniaxial magnetic platelets has been developed. The predictions of the theory agree well with experiments and provide requirements which link material properties to domain geometry. The theory is developed by assuming a model in which the domains have cylindrical walls of zero width and by then calculating the size and stability of the domains, using a straightforward although somewhat lengthy energy method. It is found that in order for domains to exist Ku⪞2πMs2, where Ku is the uniaxial anisotropy constant and Ms is the saturation magnetization. However, the model is most accurate when Ku≫2πMs2, although in this case the domains tend to have a low mobility. A formula relating domain size to the material parameters, the plate thickness and the applied bias field is obtained. More important, static stability considerations indicate that when all parameters except the bias field are held constant the domains are stable only over a 3:1 diameter range and at best a 1.6:1 bias field range. Cylindrical domains are found to be most stable for device applications when the domain radius is equal to the plate thickness which is in turn approximately equal to σw/πMs2, where σw is the wall energy density.

Novel high-temperature ferroelectric domain morphology in PbTiO3 ultrathin films

“…To our knowledge, these domains have not previously been identified in pure PbTiO 3 or for the condition of open circuit boundaries. The faceting instabilities of the nanobubble domains (Figure 6e-f) are analogous to those that occur from surface tension instabilities in thin magnetic films [48].…”

A general formalism for the determination of the effective mass of the nanoscale structural inhomogeneities of the domain wall in uniaxial ferromagnets

“…where β L is the angle coordinate of the BL center, a = 2r/h, r is the domain radius, l is the characteristic length, and S n (a) is the Thiele functions [20]. Then using Equation (3), we find that m L,BD -the effective mass of the vertical BL in the DW of magnetic bubble -can be written as…”

Instability-driven formation of domains in the intermediate state of type-I superconductors

“…By analogy with magnetic fluids, the instability of bubble domains was proposed as the mechanism of formation of ramified structures [15]. However, the progressive transformation of a circular domain into a ramified structure, which is encountered in ferromagnetic films [12] and in magnetic fluids [2], has not been reported in type-I superconductors up to now. This raises the question of how unstable NS bubbles can be produced in SC systems.…”

“…The formation of domains originates from the balance between the short-range attractive interaction associated with the interfacial tension between the two phases and long-range interactions. The regular shapes of the domains are generally not stable due to the effect of long-range interactions: lamellar domains present undulation or peristaltic instabilities [3,5,[9][10][11], circular domains (bubbles) may elongate and produce finger structures [2,4,12,13]. A crucial point for understanding the dynamics of domain patterns is to determine the contribution of these instabilities to the morphogenesis of domains [3,[14][15][16][17][18].…”